Question

Which expression is correctly developed to use the Power Rule of Exponents?
(-5)^0
(7^4)^8
12^9
(7^8) times (7^10)

Answer 1

Which of the following correctly used the Power Rule of Exponents in the expression (10^9)^7?
10^63
10^16
90^7
10^2

Answer 2

If the expression 4^10 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression?
4 times 4 times 4 times 4 times 4 times 4 times 4.
(4^2)^8
(4^12)^2
(4^5)^2

Answer 3

Use the Power Rule of Exponents to create an expression equivalent to (15^6)^2.
15^12
15^4
15^3
15^8

Answer 4

What exponent would make the two expressions equivalent: (3^3)^x = 3^24?
15
21
8
27

Answer 5

The Power Rule of Exponents states that \( (a^m)^n = a^{m \cdot n} \). The expression that correctly develops to use the Power Rule of Exponents among the options provided is:

\((7^4)^8\)

This expression can be simplified using the Power Rule:

\[
(7^4)^8 = 7^{4 \cdot 8} = 7^{32}
\]

The other expressions either do not involve a power raised to another power or are already in their simplest form according to the Power Rule.

Answer 6

To apply the Power Rule of Exponents to the expression \( (10^9)^7 \), we use the rule that states \( (a^m)^n = a^{m \cdot n} \).

Applying this rule:

\[
(10^9)^7 = 10^{9 \cdot 7} = 10^{63}
\]

Therefore, the correct expression that used the Power Rule of Exponents is:

**\(10^{63}\)**.

Answer 7

The expression \(4^{10}\) can be expanded as the product of \(4\) multiplied by itself 10 times, which is:

\[
4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4
\]

In terms of providing an equivalent expanded expression using the Power Rule of Exponents, we need to find another way to represent \(4^{10}\).

Now let’s check the options:

1. **\(4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4\)** - This is not the correct representation, as it only shows \(7\) multiplications.

2. **\((4^2)^8\)** - By applying the Power Rule:
\[
(4^2)^8 = 4^{2 \cdot 8} = 4^{16} \quad \text{(not equal to \(4^{10}\))}
\]

3. **\((4^{12})^2\)** - By applying the Power Rule:
\[
(4^{12})^2 = 4^{12 \cdot 2} = 4^{24} \quad \text{(not equal to \(4^{10}\))}
\]

4. **\((4^5)^2\)** - By applying the Power Rule:
\[
(4^5)^2 = 4^{5 \cdot 2} = 4^{10} \quad \text{(this is equal to \(4^{10}\))}
\]

The only option that correctly represents an equivalent expression for \(4^{10}\) using the Power Rule of Exponents is:

**\((4^5)^2\)**.

Answer 8

To use the Power Rule of Exponents on the expression \((15^6)^2\), we apply the rule which states that \((a^m)^n = a^{m \cdot n}\).

So we have:

\[
(15^6)^2 = 15^{6 \cdot 2} = 15^{12}
\]

Therefore, the expression equivalent to \((15^6)^2\) is:

**\(15^{12}\)**.

Answer 9

To find the exponent \(x\) that makes the expressions \((3^3)^x\) and \(3^{24}\) equivalent, we can use the Power Rule of Exponents.

Starting with the left side:

\[
(3^3)^x = 3^{3x}
\]

Now we set the exponents equal to each other since the bases are the same:

\[
3x = 24
\]

Next, we solve for \(x\):

\[
x = \frac{24}{3} = 8
\]

Thus, the exponent \(x\) that would make the two expressions equivalent is:

**8**.