Question

Which expression is equivalent tom2 -4•2^4

Answer 1

Which expression is equivalent to 2 -^5/ 2 -^1

Answer 2

Which expression is equivalent to (3 -^1)^2

Answer 3

Which expression is equivalent to (3-^6)-^5

Answer 4

Which expression is equivalent to (2-^3)^0

Answer 5

Which expression is equivalent to (5-^1)^2

Answer 6

Which expression is equivalent to 2-^1/2^2

Answer 7

Which expression is equivalent to 6-^7/6

Answer 8

Which expression is equivalent to (3-^4)^6

Answer 9

Which expression is equivalent to (5^2)0

Answer 10

Which expression is equivalent to 5-^1/5-^2

Answer 11

Which expression is equivalent to 6-^2/6^0

Answer 12

Which expression is equivalent to (6-^1)^4

Answer 13

To simplify the expression \( m^2 - 4 \cdot 2^4 \), we first evaluate \( 2^4 \):

\[
2^4 = 16
\]

Now, substitute this value back into the expression:

\[
m^2 - 4 \cdot 16
\]

Next, calculate \( 4 \cdot 16 \):

\[
4 \cdot 16 = 64
\]

Now, we can rewrite the expression:

\[
m^2 - 64
\]

Therefore, the expression \( m^2 - 4 \cdot 2^4 \) simplifies to:

\[
m^2 - 64
\]

This is the equivalent expression.

Answer 14

To simplify the expression \( 2^{-5} / 2^{-1} \), we can use the property of exponents which states that \( \frac{a^m}{a^n} = a^{m-n} \).

Applying this property:

\[
\frac{2^{-5}}{2^{-1}} = 2^{-5 - (-1)} = 2^{-5 + 1} = 2^{-4}
\]

Therefore, the expression \( 2^{-5} / 2^{-1} \) simplifies to:

\[
2^{-4}
\]

This is the equivalent expression. If you want to express it in another form, you can also write:

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

So, the equivalent expressions to \( 2^{-5} / 2^{-1} \) are \( 2^{-4} \) or \( \frac{1}{16} \).

Answer 15

To simplify the expression \( (3^{-1})^2 \), we can use the property of exponents that states \( (a^m)^n = a^{m \cdot n} \).

Applying this property:

\[
(3^{-1})^2 = 3^{-1 \cdot 2} = 3^{-2}
\]

Now, we can further express \( 3^{-2} \) as:

\[
3^{-2} = \frac{1}{3^2} = \frac{1}{9}
\]

Thus, the expression \( (3^{-1})^2 \) simplifies to:

\[
3^{-2}
\]

And in another form:

\[
\frac{1}{9}
\]

So, the equivalent expressions to \( (3^{-1})^2 \) are \( 3^{-2} \) or \( \frac{1}{9} \).

Answer 16

To simplify the expression \( (3^{-6})^{-5} \), we can use the property of exponents that states \( (a^m)^n = a^{m \cdot n} \).

Applying this property:

\[
(3^{-6})^{-5} = 3^{-6 \cdot (-5)} = 3^{30}
\]

Therefore, the expression \( (3^{-6})^{-5} \) simplifies to:

\[
3^{30}
\]

This is the equivalent expression.

Answer 17

The expression \( (2^{-3})^0 \) can be simplified using the property of exponents that states any non-zero number raised to the power of 0 is equal to 1.

Thus:

\[
(2^{-3})^0 = 1
\]

Therefore, regardless of the inside expression, as long as it is not zero, the equivalent expression for \( (2^{-3})^0 \) is:

\[
1
\]

Answer 18

To simplify the expression \( (5^{-1})^2 \), we can use the property of exponents \( (a^m)^n = a^{m \cdot n} \).

Applying this property:

\[
(5^{-1})^2 = 5^{-1 \cdot 2} = 5^{-2}
\]

Now, we can express \( 5^{-2} \) in its positive exponent form:

\[
5^{-2} = \frac{1}{5^2} = \frac{1}{25}
\]

Therefore, the expression \( (5^{-1})^2 \) simplifies to either:

\[
5^{-2}
\]

or, in another form:

\[
\frac{1}{25}
\]

So the equivalent expressions to \( (5^{-1})^2 \) are \( 5^{-2} \) or \( \frac{1}{25} \).

Answer 19

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

Applying this property:

\[
\frac{2^{-1}}{2^2} = 2^{-1 - 2} = 2^{-3}
\]

Now, we can also express \( 2^{-3} \) in a different form:

\[
2^{-3} = \frac{1}{2^3} = \frac{1}{8}
\]

Therefore, the expression \( \frac{2^{-1}}{2^2} \) simplifies to:

\[
2^{-3}
\]

or, as a fraction:

\[
\frac{1}{8}
\]

So the equivalent expressions to \( \frac{2^{-1}}{2^2} \) are \( 2^{-3} \) or \( \frac{1}{8} \).

Answer 20

To simplify the expression \( \frac{6^{-7}}{6} \), we can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).

Applying this property:

\[
\frac{6^{-7}}{6^1} = 6^{-7 - 1} = 6^{-8}
\]

Now, we can also express \( 6^{-8} \) in a different form:

\[
6^{-8} = \frac{1}{6^8}
\]

Therefore, the expression \( \frac{6^{-7}}{6} \) simplifies to:

\[
6^{-8}
\]

or, as a fraction:

\[
\frac{1}{6^8}
\]

So the equivalent expressions to \( \frac{6^{-7}}{6} \) are \( 6^{-8} \) or \( \frac{1}{6^8} \).

Answer 21

To simplify the expression \( (3^{-4})^6 \), we can use the property of exponents that states \( (a^m)^n = a^{m \cdot n} \).

Applying this property:

\[
(3^{-4})^6 = 3^{-4 \cdot 6} = 3^{-24}
\]

Now, we can also express \( 3^{-24} \) in another form:

\[
3^{-24} = \frac{1}{3^{24}}
\]

Therefore, the expression \( (3^{-4})^6 \) simplifies to:

\[
3^{-24}
\]

or, as a fraction:

\[
\frac{1}{3^{24}}
\]

So the equivalent expressions to \( (3^{-4})^6 \) are \( 3^{-24} \) or \( \frac{1}{3^{24}} \).

Answer 22

To simplify the expression \( (5^2)^0 \), we can use the property of exponents that states any non-zero number raised to the power of 0 is equal to 1.

Thus:

\[
(5^2)^0 = 1
\]

Therefore, the expression \( (5^2)^0 \) simplifies to:

\[
1
\]

So, the equivalent expression is \( 1 \).

Answer 23

To simplify the expression \( \frac{5^{-1}}{5^{-2}} \), we can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).

Applying this property, we get:

\[
\frac{5^{-1}}{5^{-2}} = 5^{-1 - (-2)} = 5^{-1 + 2} = 5^1
\]

Thus, the expression simplifies to:

\[
5^1 = 5
\]

Therefore, the equivalent expression for \( \frac{5^{-1}}{5^{-2}} \) is:

\[
5
\]

Answer 24

To simplify the expression \( \frac{6^{-2}}{6^0} \), we can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).

First, recall that \( 6^0 = 1 \).

So we have:

\[
\frac{6^{-2}}{6^0} = \frac{6^{-2}}{1} = 6^{-2}
\]

Now, we can also express \( 6^{-2} \) in another form:

\[
6^{-2} = \frac{1}{6^2} = \frac{1}{36}
\]

Therefore, the expression \( \frac{6^{-2}}{6^0} \) simplifies to:

\[
6^{-2}
\]

or, as a fraction:

\[
\frac{1}{36}
\]

So the equivalent expressions to \( \frac{6^{-2}}{6^0} \) are \( 6^{-2} \) or \( \frac{1}{36} \).

Answer 25

To simplify the expression \( (6^{-1})^4 \), we can use the property of exponents that states \( (a^m)^n = a^{m \cdot n} \).

Applying this property:

\[
(6^{-1})^4 = 6^{-1 \cdot 4} = 6^{-4}
\]

Now, we can express \( 6^{-4} \) in another form:

\[
6^{-4} = \frac{1}{6^4}
\]

Therefore, the expression \( (6^{-1})^4 \) simplifies to:

\[
6^{-4}
\]

or, as a fraction:

\[
\frac{1}{6^4}
\]

So the equivalent expressions to \( (6^{-1})^4 \) are \( 6^{-4} \) or \( \frac{1}{6^4} \).