How do you multiply and simplify #\frac { 6b } { 4b ^ { 2} } \cdot \frac { 8b ^ { 4} } { 9b ^ { 5} } #?

3 Answers
Jun 15, 2017

Answer:

See a solution process below:

Explanation:

First, rewrite this expression as:

#(6 * 8)/(4 * 9) * (b * b^4)/(b^2 * b^5)#

Next, factor and cancel common terms in the contants:

#(3 * 2 * 4 * 2)/(4 * 3 * 3) * (b * b^4)/(b^2 * b^5) =>#

#(color(red)(cancel(color(black)(3))) * 2 * color(blue)(cancel(color(black)(4))) * 2)/(color(blue)(cancel(color(black)(4))) * color(red)(cancel(color(black)(3))) * 3) * (b * b^4)/(b^2 * b^5) =>#

#(2 * 2)/3 * (b * b^4)/(b^2 * b^5) =>#

#4/3 * (b * b^4)/(b^2 * b^5)#

Now, use these rules of exponents to simplify the #b# terms in the numerator:

#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#4/3 * (b^color(red)(1) xx b^color(blue)(4) * b^4)/(b^2 * b^5) => 4/3 * (b^(color(red)(1) + color(blue)(4)))/(b^2 * b^5) => 4/3 * b^5/(b^2 * b^5) =>#

#4/3 * color(red)(cancel(color(black)(b^5)))/(b^2 * color(red)(cancel(color(black)(b^5)))) =>#

#4/(3b^2)#

Jun 15, 2017

Answer:

#(6b)/(4b^2)*(8b^4)/(9b^5)# simplifies to #color(blue)(4/(3b^2)#.

Explanation:

Multiply and simplify.

#(6b)/(4b^2)*(8b^4)/(9b^5)#

Multiply the numerators and denominators across the two fractions.

#(6bxx8b^4)/(4b^2xx9b^5)#

Multiply the coefficients.

#(6xx8xxbxxb^4)/(4xx9xxb^2xxb^5)#

Simplify.

#(48xxbxxb^4)/(36xxb^2xxb^5)#

Apply exponent product rule: #x^mx^n=x^(m+n)#.

#(48xxb^(1+4))/(36xxb^(2+5))#

Simplify.

#(48b^5)/(36b^7)#

Simplify #48/36#.

#((48-:12)b^5)/((36-:12)b^7)#

#(4b^5)/(3b^7)#

Apply quotient exponent rule: #x^m/x^n=x^(m-n)#.

#(4b^(5-7))/3#

Simplify.

#(4b^(-2))/3#

Apply the negative exponent rule: #x^(-m)=1/x^m#.

#4/(3b^2)#

Jun 15, 2017

Answer:

#4/(3b^2)#

Explanation:

Let's start with the original problem:

#(6b)/(4b^2)*(8b^4)/(9b^5)#

Let's simplify the expression by rewriting the expression and canceling out some terms:

#6/4*b/b^2*8/9*b^4/b^5=>cancel6^3/cancel4^2*b/b^2*8/9*b^4/b^5#

#8/9# can't be canceled so we will leave it as is. However, we can simplify the variable exponents by using one of the rules pertaining to exponents:

#a^-n=1/a^n#

Using this, we can simplify the expression:

#3/2*b/b^2*8/9*b^4/b^5=>3/2*b^-1*8/9*b^-1=>3/2*1/b*8/9*1/b#

We can then rearrange the expression like so:

#3/2*1/b*8/9*1/b=>3/2*8/9*1/b*1/b#

We notice that we can cancel out the #3# and the #9# and the #2# and the #8# in the two terms at the front:

#3/2*8/9*1/b*1/b=>cancel3^1/cancel2^1*cancel8^4/cancel9^3*1/b*1/b#

Then, we multiply the numerical terms and the variable terms together to obtain our answer:

#1/1*4/3*1/b*1/b=>4/3*1/b^2=>4/(3b^2)#