Evaluate. Write your answer as a whole number or as a simplified fraction.

Question

4^-2/7^-2 =_

Answer 1

To evaluate \( \frac{4^{-2}}{7^{-2}} \), we can use the property of exponents that states \( a^{-n} = \frac{1}{a^n} \).

First, rewrite \( 4^{-2} \) and \( 7^{-2} \):

\[ 4^{-2} = \frac{1}{4^2} = \frac{1}{16} \]

\[ 7^{-2} = \frac{1}{7^2} = \frac{1}{49} \]

Now, substitute these into the original expression:

\[ \frac{4^{-2}}{7^{-2}} = \frac{\frac{1}{16}}{\frac{1}{49}} \]

Dividing by a fraction is the same as multiplying by its reciprocal:

\[ \frac{1}{16} \times \frac{49}{1} = \frac{49}{16} \]

Thus, the final answer is:

\[ \frac{49}{16} \]

And as a simplified fraction, it remains \( \frac{49}{16} \).

Answer 2

10^-3 times 12 =_

Answer 3

To evaluate \( 10^{-3} \times 12 \), we first need to understand what \( 10^{-3} \) means. The expression \( 10^{-3} \) is equivalent to:

\[ 10^{-3} = \frac{1}{10^3} = \frac{1}{1000} \]

Now, we can multiply this by 12:

\[ 10^{-3} \times 12 = \frac{1}{1000} \times 12 = \frac{12}{1000} \]

Next, we simplify \( \frac{12}{1000} \):

\[ \frac{12}{1000} = \frac{3}{250} \]

Thus, the final answer is:

\[ \frac{3}{250} \]

Answer 4

12^-4 times 12^3 =_

Answer 5

To evaluate \( 12^{-4} \times 12^{3} \), we can use the property of exponents that states when multiplying two powers with the same base, we add the exponents:

\[ a^m \times a^n = a^{m+n} \]

In this case, our base \( a \) is \( 12 \), and the exponents are \( -4 \) and \( 3 \):

\[ 12^{-4} \times 12^{3} = 12^{-4 + 3} = 12^{-1} \]

Now we rewrite \( 12^{-1} \) as:

\[ 12^{-1} = \frac{1}{12} \]

Therefore, the final answer is:

\[ \frac{1}{12} \]

Answer 6

10^-2/6^-2 =_

Answer 7

To evaluate \( \frac{10^{-2}}{6^{-2}} \), we can use the property of exponents that states \( \frac{a^{-m}}{b^{-m}} = \frac{b^m}{a^m} \). Thus:

\[ \frac{10^{-2}}{6^{-2}} = \frac{6^2}{10^2} \]

Calculating each component:

\[ 6^2 = 36 \] \[ 10^2 = 100 \]

Now substituting these values back, we have:

\[ \frac{10^{-2}}{6^{-2}} = \frac{36}{100} \]

Next, we simplify \( \frac{36}{100} \):

Both 36 and 100 can be divided by 4:

\[ \frac{36 \div 4}{100 \div 4} = \frac{9}{25} \]

Thus, the final answer is:

\[ \frac{9}{25} \]

Answer 8

11^7/11^9 =_

Answer 9

To evaluate \( \frac{11^7}{11^9} \), we use the property of exponents that states:

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

In this case, \( m = 7 \) and \( n = 9 \):

\[ \frac{11^7}{11^9} = 11^{7-9} = 11^{-2} \]

Now, we can rewrite \( 11^{-2} \) as:

\[ 11^{-2} = \frac{1}{11^2} \]

Calculating \( 11^2 \):

\[ 11^2 = 121 \]

So,

\[ 11^{-2} = \frac{1}{121} \]

Thus, the final answer is:

\[ \frac{1}{121} \]

Answer 10

12^2 times 12^-1 times 12^0 =_

Answer 11

To evaluate \( 12^2 \times 12^{-1} \times 12^0 \), we will use the properties of exponents. According to the properties:

1. When multiplying powers with the same base, we add the exponents: \[ a^m \times a^n = a^{m+n} \]
2. Any number raised to the power of zero is 1: \[ a^0 = 1 \]

Now, we can evaluate the expression step by step.

First, we note that \( 12^0 = 1 \), so our expression simplifies to:

\[ 12^2 \times 12^{-1} \times 1 = 12^2 \times 12^{-1} \]

Now, we add the exponents:

\[ 12^{2 + (-1)} = 12^{2 - 1} = 12^1 \]

Finally, \( 12^1 = 12 \).

Thus, the final answer is:

\[ 12 \]