((1/2)^-3)+((1/4^-2)) ?

Question

Hi there,

how would you calculate this?:

Please show me the single steps.

Thank you.

amanvermagmat · Answer

Please note that a^-n = (1/a)^n and vice versa. 
Thus, in case of (base)^exponent: if you do reciprocal of the base then the sign of exponent changes (positive will become negative and vice versa)

Here we have (1/2)^-3 = 2^3 = 8
and (1/4)^-2 = 4^2 = 16

Adding the two, 8+16 = 24

TestPrepUnlimited · Answer

An intuitive way of dealing with negative sign "-" in exponents is to think of the negative sign "-" in exponents as a "flip" operation.

Problem: ((1/2)^-3)+((1/4)^-2))

Step 1: Apply the - sign and flip 1/2 and 1/4.
=(2^3)+(4^2)

Step 2: Apply the remaining exponent:
=8+16
=24

Problem: ((1/2)^-3)+((1/4^-2))

Step 1: Apply the - sign and flip 1/2 and 4
=(2^3)+(1/(1/4)^2)

Step 2: Apply the remaining exponent:
=8+(1/(1/16)
=8+16

broall · Answer

Answer with math format

$\big (\frac{1}{2} \big )^{-3}+\big (\frac{1}{4}\big )^{-2}=\frac{1}{\big (\frac{1}{2} \big )^{3}}+\frac{1}{\big (\frac{1}{4}\big )^{2}}=\frac{1}{\frac{1}{2^3}}+\frac{1}{\frac{1}{4^2}}=2^3+4^2=8+16=24$

ScottTargetTestPrep · Answer

Solution:
 
((1/2)^-3) + ((1/4^-2)) = ?
 
2^3 + 4^2
 
2^3 + (2^2)^2
 
2^3 + 2^4 = 8 + 16 = 24

((1/2)^-3)+((1/4^-2)) ?

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