Question

Help this is due at 11 (ACTUALLY THIS IS REAL)

Answer 1

Answer:
`a^5`

Explanation:

`\sqrt[3]{a^15}` is basically another way of writing
`a^15 / a^3` which is just 15/3 to give you 5

Answer 2

1st one:
`1.804 * 10^7`

2nd one:
`\sf a^5`

Explanation:

1st part:

Product in Scientific Notation:

To find the product of 41 and
`\sf 4.4 * 10^5` in scientific notation, follow these steps:

`\sf 41 * (4.4 * 10^5) = (41 * 4.4) * 10^5`

Calculate the numerical part:

`\sf 41 * 4.4 = 180.4`

So, the product in scientific notation is:

`\begin{aligned} 1.804 * 10^2 * 10^5 & = 1.804 * 10^(2+5) \\\\ & = \boxed{1.804 } * 10^{\boxed{\sf 7 }} \end{aligned}`

2nd Part:

Simplifying
`\sf \sqrt[3]{a^(15)}`:

The property used here is the rule for exponentiation when we have a power raised to another power. The rule is:

`\sf (a^m)^n = a^(mn)`

In wer case,
`\sf \sqrt[3]{a^(15)}` means raising
`\sf a^(15)` to the power of
`\sf (1)/(3)` because the cube root is the same as raising to the power of
`\sf (1)/(3)`. So, applying the exponent rule:

`\sf (a^(15))^{(1)/(3)} = a^{15 * (1)/(3)} \\\\ = a^5`

Therefore,
`\sf \sqrt[3]{a^(15)}` simplifies to
`\sf a^5`. This is based on the property that when we take the cube root of a number raised to a power, we divide the exponent by the root.