25 answers
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.
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 \( \frac{1}{16} \).
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 \( \frac{1}{9} \).
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.
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:
\[ 1 \]
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 \( \frac{1}{25} \).
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 \( \frac{1}{8} \).
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 \( \frac{1}{6^8} \).
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 \( \frac{1}{3^{24}} \).
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 \( 1 \).
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:
\[ 5 \]
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 \( \frac{1}{36} \).
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 \( \frac{1}{6^4} \).
