Question

Which expression is equivalent to StartFraction 7 Superscript 5 Over 7 squared EndFraction?
(7 times 5) (7 times 2)
(7 times 7 times 7 times 7 times 7) (7 times 7)
StartFraction 7 times 5 Over 7 times 2 EndFraction
StartFraction 7 times 7 times 7 times 7 times 7 Over 7 times 7 EndFraction

Answer 1

To simplify the expression \(\frac{7^5}{7^2}\), we can use the property of exponents that states \(\frac{a^m}{a^n} = a^{m-n}\).

Applying this property:

\[
\frac{7^5}{7^2} = 7^{5-2} = 7^3
\]

Now, let's check which of the provided options is equivalent to \(7^3\):

1. \((7 \times 5) (7 \times 2)\) — This does not represent \(7^3\).
2. \((7 \times 7 \times 7 \times 7 \times 7) (7 \times 7)\) — This represents \(7^5 \times 7^2\), which is not equivalent to \(7^3\).
3. \(\frac{7 \times 5}{7 \times 2}\) — This does not simplify to \(7^3\).
4. \(\frac{7 \times 7 \times 7 \times 7 \times 7}{7 \times 7}\) — This is \(\frac{7^5}{7^2} = 7^{5-2} = 7^3\).

The correct option that is equivalent to \(\frac{7^5}{7^2}\) is:

\[
\text{StartFraction 7 times 7 times 7 times 7 times 7 Over 7 times 7 EndFraction}
\]