Apply the Property of Negative Integer Exponents to solve 3^−4 . The answer should not contain any exponent expression or decimals.
To apply the property of negative integer exponents, we use the following rule:
$$a^{-n} = \frac{1}{a^n}$$
Using this rule, we can solve the expression 3^(-4):
$$3^{-4} = \frac{1}{3^4}$$
And finally:
$$3^{-4} = \frac{1}{81}$$
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7−3⋅7−5 with positive exponents only.(1 point)
To apply the property of negative integer exponents, we use the following rule:
$$a^{-n} = \frac{1}{a^n}$$
Using this rule for the expression $7^{-3} \cdot 7^{-5}$, we can rewrite it as:
$$\frac{1}{7^3} \cdot \frac{1}{7^5}$$
To simplify this expression further, we multiply the fractions:
$$\frac{1}{7^3} \cdot \frac{1}{7^5} = \frac{1}{7^{3+5}}$$
Now we can simplify the exponent:
$$\frac{1}{7^{3+5}} = \frac{1}{7^8}$$
So, an expression equivalent to $7^{-3} \cdot 7^{-5}$ with positive exponents only is $1/7^8$.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5−94−12 with positive exponents only.(1 point)
To apply the property of negative integer exponents, we use the following rule:
$$a^{-n} = \frac{1}{a^n}$$
Using this rule for the expression $5^{-9} \cdot 4^{-12}$, we can rewrite it as:
$$\frac{1}{5^9} \cdot \frac{1}{4^{12}}$$
Now we need to simplify the exponents:
$$\frac{1}{5^9} \cdot \frac{1}{4^{12}} = \frac{1}{5^9} \cdot \frac{1}{(2^2)^{12}} = \frac{1}{5^9} \cdot \frac{1}{2^{24}}$$
And finally, we can write the expression with positive exponents only:
$$\frac{1}{5^9} \cdot \frac{1}{2^{24}} = \frac{1}{(5^9) \cdot (2^{24})}$$
Therefore, an expression equivalent to $5^{-9} \cdot 4^{-12}$ with positive exponents only is $1/(5^9 \cdot 2^{24})$.
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I apologize for the mistake. Let's correct the solution.
To apply the property of negative integer exponents, we use the following rule:
$$a^{-n} = \frac{1}{a^n}$$
Using this rule for the expression $5^{-9} \cdot 4^{-12}$, we can rewrite it as:
$$\frac{1}{5^9} \cdot \frac{1}{4^{12}}$$
Now we need to simplify the exponents:
$$\frac{1}{5^9} \cdot \frac{1}{4^{12}} = \frac{1}{5^9} \cdot \frac{1}{(2^2)^{12}} = \frac{1}{5^9} \cdot \frac{1}{2^{24}}$$
To simplify this further, we can rewrite $2^{24}$ as $(2^6)^4$:
$$\frac{1}{5^9} \cdot \frac{1}{2^{24}} = \frac{1}{5^9} \cdot \frac{1}{(2^6)^4}$$
Now we can apply the property again and simplify the exponents:
$$\frac{1}{5^9} \cdot \frac{1}{(2^6)^4} = \frac{1}{5^9} \cdot \frac{1}{2^{6 \cdot 4}}$$
$$ = \frac{1}{5^9} \cdot \frac{1}{2^{24}}$$
Therefore, an expression equivalent to $5^{-9} \cdot 4^{-12}$ with positive exponents only is $1/(5^9 \cdot 2^{24})$.