Asked by Alexsandra Huerta on Mar 10, 2024

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Evaluate 64−4/364 ^ { - 4 / 3 }644/3 without using a calculator.

A) 1512\frac { 1 } { 512 }5121
B) 64
C) 164\frac { 1 } { 64 }641
D) 1256\frac { 1 } { 256 }2561
E) 256

Evaluate

The process of calculating the value of an expression, equation, or function for given variables or numbers.

Calculator

An electronic or manual device used for calculating numbers, functions, and mathematical expressions.

Exponents

Exponents indicate how many times a number, the base, is multiplied by itself.

  • Interpret expressions without deploying calculative electronic devices.
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Verified Answer

JV
Jayme Viers

Mar 10, 2024

Final Answer :
D
Explanation :
First we will write 64−4/364 ^ { - 4 / 3 }644/3 in the form of 1644/3\frac{1}{64^{4/3}}644/31 .

Now, we know that 64=4364 = 4^364=43 , so we can rewrite this as 1(43)4/3\frac{1}{(4^3)^{4/3}}(43)4/31 .

Using the exponent rule of (ab)c=abc(a^b)^c = a^{bc}(ab)c=abc , we simplify to get 144\frac{1}{4^{4}}441 .

Therefore, 64−4/3=125664 ^ { - 4 / 3 } = \frac { 1 } { 256 }644/3=2561 .