How do you evaluate #(- \frac { 3} { 4} ) ^ { 3} \times ( - 8) ^ { 2}#?

2 Answers
Leeor H.
Dec 24, 2016

#-27#

Explanation:

#(−3/4)^3# is the same thing as #(−3/4) * (−3/4) * (−3/4)#

If you multiply straight across, and take into consideration that 3 negatives equals a negative, then the first part is the same thing as #(-27/64)#.

The second part, #(-8)^2#, is saying #-8 * -8#, which is positive 64 since a negative times a negative is a positive. Now you can multiply the two parts together:

#-27/64 * 64/1#

#-27/1# (because the 64 on the top and bottom cancel out)

the answer is #-27#.

Shell
Dec 24, 2016

#-27#

Explanation:

#(-3/4)^3 * (-8)^2#

A number to the third power (cubed) is the number multiplied by itself three times. A number to the second power (squared) is the number multiplied by itself two times.

A negative number raised to an odd power is negative and a negative number raised to an even power is positive.

#(-3/4)(-3/4)(-3/4) xx (-8)*(-8)#

#-27/64xx64#

#-27/cancel64xxcancel64#

#-27#

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