Question

use the product rule of exponents to simplify 5^10 x 5^5

a. 25^15
b. 5^50
c. 25^50
d. 5^15
Answer
find the numerical equivalent of 9^9 x 9^6. Your answer should be written without exponents.
Answer
what is the missing exponent in the following equation?

h^450/h^? = h^215
Answer
simplify 12^87 divided 12^25
Answer
what is the missing number in this simplified exponential expression: 7^? divided 7^5 = 7^12?

Answer
what is the value of 6.9 - 2^0?

a. 7.9
b. 5.9
c. 6.9
d. 4.9
Answered by GPT-4o mini
To simplify \( 5^{10} \times 5^5 \) using the product rule of exponents, which states that \( a^m \times a^n = a^{m+n} \), we add the exponents:

\[
5^{10} \times 5^5 = 5^{10+5} = 5^{15}
\]

So, the simplified expression is \( 5^{15} \).

The correct answer is:

**d. \( 5^{15} \)**
Answered by GPT-4o mini
To calculate \( 9^9 \times 9^6 \), we can use the product rule of exponents, which states that \( a^m \times a^n = a^{m+n} \).

So, we have:

\[
9^9 \times 9^6 = 9^{9+6} = 9^{15}
\]

Now, we need to find the numerical equivalent of \( 9^{15} \).

Calculating \( 9^{15} \):

1. First, we can express \( 9 \) as \( 3^2 \):
\[
9^{15} = (3^2)^{15} = 3^{30}
\]

2. Now, calculate \( 3^{30} \). Since this is quite a large number, it's often easier to use a calculator for such calculations. However, we can break it down:
\[
3^{30} = (3^{10})^3
\]
and
\[
3^{10} = 59049
\]

So,
\[
3^{30} = 59049^3
\]

Calculating \( 59049^3 \), we find:

\[
59049^3 = 205891132094649
\]

Thus, \( 9^{15} = 205891132094649 \).

So, the numerical equivalent of \( 9^9 \times 9^6 \) is:

**205891132094649**.
Answered by GPT-4o mini
To solve the equation

\[
\frac{h^{450}}{h^{?}} = h^{215},
\]

we can use the quotient rule of exponents, which states that

\[
\frac{a^m}{a^n} = a^{m-n}.
\]

Applying this rule, we can rewrite the left side:

\[
h^{450 - ?} = h^{215}.
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
450 - ? = 215.
\]

To find the missing exponent (?), we can rearrange this equation:

\[
? = 450 - 215.
\]

Calculating that gives:

\[
? = 235.
\]

Thus, the missing exponent is **235**.
Answered by GPT-4o mini
To simplify \( \frac{12^{87}}{12^{25}} \), we can use the quotient rule of exponents, which states that \( \frac{a^m}{a^n} = a^{m-n} \).

Applying this rule:

\[
\frac{12^{87}}{12^{25}} = 12^{87 - 25} = 12^{62}.
\]

Thus, the simplified expression is \( 12^{62} \).
Answered by GPT-4o mini
To find the missing number in the exponential expression

\[
\frac{7^{?}}{7^5} = 7^{12},
\]

we can use the quotient rule of exponents, which states that

\[
\frac{a^m}{a^n} = a^{m-n}.
\]

Applying this rule, we have:

\[
7^{? - 5} = 7^{12}.
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
? - 5 = 12.
\]

To solve for the missing number (?), we can rearrange the equation:

\[
? = 12 + 5.
\]

Calculating that gives:

\[
? = 17.
\]

Thus, the missing number is **17**.
Answered by GPT-4o mini
To calculate \( 6.9 - 2^0 \), we first need to evaluate \( 2^0 \).

Any non-zero number raised to the power of 0 is equal to 1. Therefore:

\[
2^0 = 1.
\]

Now, we can substitute that back into the equation:

\[
6.9 - 1 = 5.9.
\]

So the value of \( 6.9 - 2^0 \) is:

**5.9**.

The correct answer is **b. 5.9**.