which expression is equal to 8 to the power of 6 over 4 to the power of 6

Question

1 over 2 to the power of 6
2 to the power of 6
2 to the power of 0
2

Answer 1

To simplify the expression \( \frac{8^6}{4^6} \), we can rewrite the bases in terms of powers of 2.

First, note that:

• \( 8 = 2^3 \)
• \( 4 = 2^2 \)

Now we can rewrite the expression:

\[ 8^6 = (2^3)^6 = 2^{3 \cdot 6} = 2^{18} \]

\[ 4^6 = (2^2)^6 = 2^{2 \cdot 6} = 2^{12} \]

Now substitute these back into the original expression:

\[ \frac{8^6}{4^6} = \frac{2^{18}}{2^{12}} \]

Using the properties of exponents, we can simplify:

\[ \frac{2^{18}}{2^{12}} = 2^{18 - 12} = 2^6 \]

Thus, \( \frac{8^6}{4^6} = 2^6 \).

Therefore, the correct answer is:

2 to the power of 6.

Answer 2

correct! now what's the expression equal to 10 to the power of 9 times 10 to the power of -7?
1 over 10 to the power of -2
10 to the power of -63
1 over 10 to the power of -63
1 over 10 to the power of 2

Answer 3

To simplify the expression \( 10^9 \times 10^{-7} \), we can use the properties of exponents. Specifically, when multiplying numbers with the same base, we add the exponents:

\[ 10^9 \times 10^{-7} = 10^{9 + (-7)} = 10^{9 - 7} = 10^2 \]

So, \( 10^9 \times 10^{-7} = 10^2 \).

Now, among your options, we can see that \( 10^2 \) is not explicitly listed, but if we want to look at it in an inverse form and express \( 10^2 \) differently with negative exponents, we can rewrite \( 10^2 \) as:

\[ 10^2 = \frac{1}{10^{-2}} \]

However, comparing with the options given, \( 1 \) over \( 10^{-2} \) can be rearranged by multiplying both the numerator and denominator by \( 10^{2} \):

Thus, the correct answer is:

1 over 10 to the power of -2.

Answer 4

correct again! great work! now what's the expression equal to (12 to the power of 3) to the power of 4?

1 over 12 to the power of 7
1 over 12 to the power of 12
12 to the power of 7
12 to the power of 12

Answer 5

To simplify the expression \( (12^3)^4 \), we can use the power of a power property of exponents, which states that \( (a^m)^n = a^{m \cdot n} \).

Applying this property:

\[ (12^3)^4 = 12^{3 \cdot 4} = 12^{12} \]

Therefore, \( (12^3)^4 = 12^{12} \).

Among your provided options, the correct answer is:

12 to the power of 12.

Answer 6

thanks so much bot! great work! again!!! Which expression is equivalent to 8 to the power of -4 over 4 to the power of -4?

2 to the power of -4
2 to the power of 0
2
1 over 2 to the power of -4

Answer 7

To simplify the expression \( \frac{8^{-4}}{4^{-4}} \), we can rewrite 8 and 4 in terms of base 2:

\[ 8 = 2^3 \quad \text{and} \quad 4 = 2^2 \]

Now we can express both terms:

\[ 8^{-4} = (2^3)^{-4} = 2^{3 \cdot -4} = 2^{-12} \]

\[ 4^{-4} = (2^2)^{-4} = 2^{2 \cdot -4} = 2^{-8} \]

Next, we substitute these back into the original expression:

\[ \frac{8^{-4}}{4^{-4}} = \frac{2^{-12}}{2^{-8}} \]

Using the properties of exponents, we can simplify:

\[ \frac{2^{-12}}{2^{-8}} = 2^{-12 - (-8)} = 2^{-12 + 8} = 2^{-4} \]

Thus, \( \frac{8^{-4}}{4^{-4}} = 2^{-4} \).

Among your options, the correct answer is:

2 to the power of -4.