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Answer:

#140#

Explanation:

Use PEMDAS to help with the order of operations:

P for Parentheses

E for Exponents

MD for Multiplication and Division (left to right)

AS for Addition and Subtraction (left to right)

So we find:

#(4xx4(6+4)-3(8+1)+2)-:3+(5+2)(5+2)-2xx2+(42-:6)(42-:6)+1#

#=(4xx4(10)-3(9)+2)-:3+(7)(7)-2xx2+(7)(7)+1#

#=(4xx40-27+2)-:3+49-2xx2+49+1#

#=(160-27+2)-:3+49-2xx2+49+1#

#=(133+2)-:3+49-2xx2+49+1#

#=135-:3+49-2xx2+49+1#

#=45+49-4+49+1#

#=94-4+49+1#

#=90+49+1#

#=139+1#

#=140#

Answer:

#= 1/2^2#

#=1/4#

Explanation:

As soon as there are indices, you cannot cancel any of the bases.

Working out each factor to its actual value is not practical - the values are far too big.

Write each base as the product of its prime factors.
You might have noticed that all the bases are powers of 2.

#color(red)(4 = 2^2)#
#color(blue)(8= 2^3)#
#color(purple)(16= 2^4)#
#color(forestgreen)(32=2^5)#

#(color(red)(4)^10*color(blue)(8)^-3*color(purple)(16)^-2)/color(forestgreen)(32)#

#=(color(red)((2^2))^10*color(blue)((2^3))^-3*color(purple)((2^4))^-2)/color(forestgreen)((2^5))#

Multiply the indices: #(x^m)^n = x^(mxxn)#

#=(color(red)(2^20)*color(blue)(2^-9)*color(purple)(2^-8))/color(forestgreen)((2^5))#

Add the indices of like bases: #x^m xx x^n = x^(m+n)#

#=2^3/2^5#

#= 1/2^2#

#=1/4#

Answer:

#s=4/15#

Explanation:

Isolate s by adding #2/3# to both sides of the equation.

Adding the same value to both sides retains the 'balance' of the equation.

#-2/5color(red)(+2/3)=cancel(-2/3)color(red)cancel(+2/3)+s#

#rArrs=-2/5+2/3larrcolor(magenta)"reversing the equation"#

Before we can add these fractions we require them to have a
#color(blue)"common denominator"#

Multiplying the numerator/denominator of the first fraction by 3 and multiplying the numerator/denominator of the second fraction by 5, gives a common denominator.

#rArrs=(-2/5xx3/3)+(2/3xx5/5)#

#color(white)(xxxx)=-6/15+10/15larrcolor(red)" common denominator"#

Now the denominators are the same we can add the numerators.

#rArrs=(-6+10)/15=4/15#

Answer:

#56,700,000=5.67xx10^7#

Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of #10#.

Note that moving decimal #p# digits to right is equivalent to multiplying by #10^p# and moving decimal #q# digits to left is equivalent to dividing by #10^q#.

Hence, we should either divide the number by #10^p# i.e. multiply by #10^(-p)# (if moving decimal to right) or multiply the number by #10^q# (if moving decimal to left).

In other words, it is written as #axx10^n#, where #1<=a<10# and #n# is an integer.

To write #56,700,000# in scientific notation, we will have to move the decimal point seven points to the left, which literally means dividing by #10^7#.

Hence in scientific notation #56,700,000=5.67xx10^7# (note that as we have moved decimal seven points to the left we are multiplying by #10^7#.

What is 5/8 +7/8 ?

Jim G.
Jim G.
Featured 4 weeks ago

Answer:

#12/8=3/2#

Explanation:

To add 2 fractions we require the #color(blue)"denominators"# to be the same value.

In this case they are, both 8

We can therefore #color(blue)"add the numerators"# while leaving the denominator as it is.

#rArr5/8+7/8#

#=(5+7)/8#

#=12/8#

We can #color(blue)"simplify"# the fraction by dividing the numerator/denominator by the #color(blue)"highest common factor"# of 12 and 8, which is 4

#rArr12/8=(12÷4)/(8÷4)=3/2larrcolor(red)" in simplest form"#

This process is normally done using #color(blue)"cancelling"#

#rArr12/8=cancel(12)^3/cancel(8)^2=3/2larrcolor(red)" in simplest form"#

A fraction is in #color(blue)"simplest form"# when no other factor but 1 divides into the numerator/denominator.

Answer:

#3 49/144#

Explanation:

There are 2 possible approaches to this calculation, both made fairly 'awkward' due to the values on the denominators of the fractions.

#color(red)"Approach 1"#

Change the #color(blue)"mixed numbers " "to "color(blue)"improper fractions"#

#rArr5 1/16=81/16" and "1 13/18=31/18#

The calculation is now.

#81/16-31/18#

Before we can subtract the fractions we require them to have a
#color(blue)"common denominator"#

We have to find the #color(blue)"lowest common multiple"# ( LCM) of 16 and 18

The LCM of 16 and 18 is 144

#rArr81/16xx9/9=729/144" and "31/18xx8/8=248/144#

#rArr729/144-248/144larrcolor(red)" is now the calculation"#

Since the denominators are now common we can subtract the numerators, leaving the denominator as it is.

#rArr729/144-248/144=(729-248)/144#

#=481/144=3 49/144larrcolor(red)" returning a mixed number"#

#color(red)"Approach 2"#

#"Using the fact that "5 1/16=5+1/16;1 13/18=1+13/18#

#"Then "5 1/16-1 13/18#

#=5+1/16-(1+13/18)=5+1/16-1-13/18#

We can now subtract the numbers and subtract the fractions separately.

#rArr5+1/16-1-13/18=(5-1)+1/16-13/18#

#=4+(1/16xx9/9-13/18xx8/8)#

#=4+(9/144-104/144)#

#=4+(-95/144)#

#=4-95/144#

#=576/144-95/144#

#=481/144#

#=3 49/144larrcolor(red)" as a mixed number"#

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