Which expression is equivalent to 6^7/6^8x6-^7

Answer 1

To simplify the expression \( \frac{6^7}{6^8 \times 6^{-7}} \), we can use the properties of exponents.

1. First, we can combine the exponents in the denominator using the property \( a^m \times a^n = a^{m+n} \): \[ 6^8 \times 6^{-7} = 6^{8 + (-7)} = 6^{8 - 7} = 6^{1} = 6 \]

2. Now the expression simplifies to: \[ \frac{6^7}{6} \]

3. We can apply the property \( \frac{a^m}{a^n} = a^{m-n} \): \[ \frac{6^7}{6^1} = 6^{7 - 1} = 6^6 \]

Thus, the expression \( \frac{6^7}{6^8 \times 6^{-7}} \) simplifies to \( 6^6 \).

So, the equivalent expression is \( 6^6 \).

Answer 2

Which expression is equivalent to 4^2/4^3•4^0

Answer 3

To simplify the expression \( \frac{4^2}{4^3 \cdot 4^0} \), we can use the properties of exponents.

1. First, simplify \( 4^3 \cdot 4^0 \) using the property \( a^m \cdot a^n = a^{m+n} \): \[ 4^3 \cdot 4^0 = 4^{3 + 0} = 4^3 \]

2. Now the expression simplifies to: \[ \frac{4^2}{4^3} \]

3. Next, we can apply the property \( \frac{a^m}{a^n} = a^{m-n} \): \[ \frac{4^2}{4^3} = 4^{2 - 3} = 4^{-1} \]

4. Finally, we can express \( 4^{-1} \) as: \[ 4^{-1} = \frac{1}{4} \]

Thus, the expression \( \frac{4^2}{4^3 \cdot 4^0} \) simplifies to \( 4^{-1} \) or \( \frac{1}{4} \).

So, the equivalent expression is \( \frac{1}{4} \).

Answer 4

Which expression is equivalent to (3-^1/3^6) -^5

Answer 5

To simplify the expression \( \left( \frac{3^{-1}}{3^6} \right)^{-5} \), we can follow these steps:

1. Simplify the fraction inside the parentheses: Using the property \(\frac{a^m}{a^n} = a^{m-n}\), we can simplify \(\frac{3^{-1}}{3^6}\): \[ \frac{3^{-1}}{3^6} = 3^{-1 - 6} = 3^{-7} \]

2. Now replace the fraction in the original expression: The expression now looks like: \[ (3^{-7})^{-5} \]

3. Apply the power of a power property: Using the property \((a^m)^n = a^{m \cdot n}\): \[ (3^{-7})^{-5} = 3^{-7 \cdot -5} = 3^{35} \]

Thus, the expression \( \left( \frac{3^{-1}}{3^6} \right)^{-5} \) simplifies to \( 3^{35} \).

The equivalent expression is \( 3^{35} \).

Answer 6

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

Answer 7

To simplify the expression \( \left( \frac{2^0}{2} \right)^2 \), we can follow these steps:

1. Evaluate \(2^0\): By the property of exponents, any non-zero number raised to the power of 0 is 1: \[ 2^0 = 1 \]

2. Substitute into the fraction: Now substitute \(2^0\) into the expression: \[ \frac{2^0}{2} = \frac{1}{2} \]

3. Now, replace the fraction in the original expression: The expression now looks like: \[ \left( \frac{1}{2} \right)^2 \]

4. Square the fraction: Squaring the fraction results in: \[ \left( \frac{1}{2} \right)^2 = \frac{1^2}{2^2} = \frac{1}{4} \]

Thus, the expression \( \left( \frac{2^0}{2} \right)^2 \) simplifies to \( \frac{1}{4} \).

The equivalent expression is \( \frac{1}{4} \).

Answer 8

Which expression is equivalent to (6^0)^4/6^5

Answer 9

To simplify the expression \( \frac{(6^0)^4}{6^5} \), we can follow these steps:

1. Evaluate \(6^0\): By the property of exponents, any non-zero number raised to the power of 0 is 1: \[ 6^0 = 1 \]

2. Replace \(6^0\) in the expression: The expression now looks like: \[ (6^0)^4 = 1^4 = 1 \]

3. Substitute back into the fraction: The expression simplifies to: \[ \frac{1}{6^5} \]

Thus, the expression \( \frac{(6^0)^4}{6^5} \) simplifies to \( \frac{1}{6^5} \).

The equivalent expression is \( \frac{1}{6^5} \).

Answer 10

Which expression is equivalent to 5-^1/5-^2 • 5-^3

Answer 11

To simplify the expression \( \frac{5^{-1}}{5^{-2} \cdot 5^{-3}} \), we can use the properties of exponents.

1. Simplify the denominator: Use the property \( a^m \cdot a^n = a^{m+n} \) to combine the powers in the denominator: \[ 5^{-2} \cdot 5^{-3} = 5^{-2 + (-3)} = 5^{-2 - 3} = 5^{-5} \]

2. Now rewrite the expression: The expression now looks like: \[ \frac{5^{-1}}{5^{-5}} \]

3. Apply the property of exponents: Use the property \( \frac{a^m}{a^n} = a^{m-n} \): \[ \frac{5^{-1}}{5^{-5}} = 5^{-1 - (-5)} = 5^{-1 + 5} = 5^{4} \]

Hence, the simplified expression \( \frac{5^{-1}}{5^{-2} \cdot 5^{-3}} \) is equivalent to \( 5^4 \).