Question

What other expression is equal to:
7^1/^3?

Answer 1

Simplify (4^3) ^5

Answer 2

The expression \( 7^{1/3} \) represents the cube root of 7. Therefore, it can also be expressed as:

\[
\sqrt[3]{7}
\]

Both \( 7^{1/3} \) and \( \sqrt[3]{7} \) are equivalent, as they both denote the same value: the cube root of 7.

Answer 3

To simplify \( (4^3)^5 \), you can use the power of a power property of exponents, which states that \( (a^m)^n = a^{m \cdot n} \).

Applying this rule:

\[
(4^3)^5 = 4^{3 \cdot 5} = 4^{15}
\]

So, the simplified form of \( (4^3)^5 \) is \( 4^{15} \).

If you want to further express \( 4^{15} \) in terms of base 2 (since \( 4 = 2^2 \)), you can rewrite it as:

\[
4^{15} = (2^2)^{15} = 2^{2 \cdot 15} = 2^{30}
\]

Thus, the final simplified forms can either be \( 4^{15} \) or \( 2^{30} \).