Asked by mechanic
\frac{1}{7^3}\times \frac{1}{7^5}=
Answers
Answered by
GPT 3.5
To solve this expression, we can simplify the fractions first. We have:
$$\frac{1}{7^3}\times \frac{1}{7^5} = \frac{1}{7^{3+5}}$$
Now we can simplify the exponent:
$$\frac{1}{7^{3+5}} = \frac{1}{7^8}$$
Therefore, the final answer is $\frac{1}{7^8}$
$$\frac{1}{7^3}\times \frac{1}{7^5} = \frac{1}{7^{3+5}}$$
Now we can simplify the exponent:
$$\frac{1}{7^{3+5}} = \frac{1}{7^8}$$
Therefore, the final answer is $\frac{1}{7^8}$
Answered by
GPT 3.5
To simplify the expression $\frac{1}{7^3}\times \frac{1}{7^5}$, we can combine the fractions by multiplying the numerators and denominators. This gives us $\frac{1}{7^{3+5}}$. Simplifying further, we find that the expression is equal to $\frac{1}{7^8}$.
Answered by
GPT 3.5
To simplify the expression 1 over 7 cubed times 1 over 7 to the fifth power, we can combine these fractions by multiplying the numerators and denominators. This gives us 1 over 7 to the power of 3 plus 5. Simplifying further, we find that the expression is equal to 1 over 7 to the power of 8.
Answered by
GPT 3.5
To simplify the expression \(\frac{5^{-9}}{4^{-12}}\), we can rewrite it using the rules of exponents. Recall that \(a^{-b} = \frac{1}{a^{b}}\). Applying this rule to the given expression, we have:
\(\frac{5^{-9}}{4^{-12}} = \frac{1}{5^9} \cdot \frac{1}{4^{-12}}\)
Using the rule \(a^m \cdot a^n = a^{m+n}\), we can combine the fractions:
\(\frac{1}{5^9} \cdot \frac{1}{4^{-12}} = \frac{1}{5^9 \cdot 4^{-12}}\)
To simplify the denominator further, we can use the rule \(\frac{1}{a^m} = a^{-m}\):
\(\frac{1}{5^9 \cdot 4^{-12}} = \frac{1}{5^9 \cdot \frac{1}{4^{12}}} = \frac{1}{5^9 \cdot 4^{12}}\)
So, the simplified expression is \(\frac{1}{5^9 \cdot 4^{12}}\).
\(\frac{5^{-9}}{4^{-12}} = \frac{1}{5^9} \cdot \frac{1}{4^{-12}}\)
Using the rule \(a^m \cdot a^n = a^{m+n}\), we can combine the fractions:
\(\frac{1}{5^9} \cdot \frac{1}{4^{-12}} = \frac{1}{5^9 \cdot 4^{-12}}\)
To simplify the denominator further, we can use the rule \(\frac{1}{a^m} = a^{-m}\):
\(\frac{1}{5^9 \cdot 4^{-12}} = \frac{1}{5^9 \cdot \frac{1}{4^{12}}} = \frac{1}{5^9 \cdot 4^{12}}\)
So, the simplified expression is \(\frac{1}{5^9 \cdot 4^{12}}\).
Answered by
GPT 3.5
To simplify the expression \(\frac{5^{-9}}{4^{-12}}\), we can rewrite it using the rules of exponents.
Recall that \(a^{-b} = \frac{1}{a^b}\). Applying this rule to the given expression, we have:
\(\frac{5^{-9}}{4^{-12}} = \frac{1}{5^9} \cdot \frac{1}{4^{-12}}\)
Now, using the rules of multiplication with exponents, we can combine the fractions:
\(\frac{1}{5^9} \cdot \frac{1}{4^{-12}} = \frac{1}{5^9 \cdot 4^{-12}}\)
To simplify the denominator further, we can use the rule \(\frac{1}{a^m} = a^{-m}\):
\(\frac{1}{5^9 \cdot 4^{-12}} = \frac{1}{5^9 \cdot \frac{1}{4^{12}}} = \frac{1}{5^9 \cdot 4^{12}}\)
So, the simplified expression is \(\frac{1}{5^9 \cdot 4^{12}}\).
Recall that \(a^{-b} = \frac{1}{a^b}\). Applying this rule to the given expression, we have:
\(\frac{5^{-9}}{4^{-12}} = \frac{1}{5^9} \cdot \frac{1}{4^{-12}}\)
Now, using the rules of multiplication with exponents, we can combine the fractions:
\(\frac{1}{5^9} \cdot \frac{1}{4^{-12}} = \frac{1}{5^9 \cdot 4^{-12}}\)
To simplify the denominator further, we can use the rule \(\frac{1}{a^m} = a^{-m}\):
\(\frac{1}{5^9 \cdot 4^{-12}} = \frac{1}{5^9 \cdot \frac{1}{4^{12}}} = \frac{1}{5^9 \cdot 4^{12}}\)
So, the simplified expression is \(\frac{1}{5^9 \cdot 4^{12}}\).
Answered by
GPT 3.5
To simplify \(5^{-9} \div 4^{-12}\), we can rewrite it using the rules of exponents.
Remember that \(a^{-b} = \frac{1}{a^b}\). Applying this rule to the given expression, we have:
\(5^{-9} \div 4^{-12} = \frac{1}{5^9} \div \frac{1}{4^{12}}\)
Now, inverting the divisor and applying the rule for dividing fractions, we get:
\(\frac{1}{5^9} \div \frac{1}{4^{12}} = \frac{1}{5^9} \times \frac{4^{12}}{1}\)
By using the rule \(a^m \times a^n = a^{m+n}\), we can simplify further:
\(\frac{1}{5^9} \times \frac{4^{12}}{1} = \frac{4^{12}}{5^9}\)
So, \(5^{-9} \div 4^{-12}\) simplifies to \(\frac{4^{12}}{5^9}\).
Remember that \(a^{-b} = \frac{1}{a^b}\). Applying this rule to the given expression, we have:
\(5^{-9} \div 4^{-12} = \frac{1}{5^9} \div \frac{1}{4^{12}}\)
Now, inverting the divisor and applying the rule for dividing fractions, we get:
\(\frac{1}{5^9} \div \frac{1}{4^{12}} = \frac{1}{5^9} \times \frac{4^{12}}{1}\)
By using the rule \(a^m \times a^n = a^{m+n}\), we can simplify further:
\(\frac{1}{5^9} \times \frac{4^{12}}{1} = \frac{4^{12}}{5^9}\)
So, \(5^{-9} \div 4^{-12}\) simplifies to \(\frac{4^{12}}{5^9}\).
Answered by
GPT 3.5
Apologies for the confusion. Let's simplify the expression \(5^{-9} \div 4^{-12}\) without using any code.
To divide two numbers with the same base but different exponents, we subtract the exponents. So, the expression can be rewritten as \(5^{-9 - (-12)}\).
To subtract the exponents, we change the sign of the second exponent and add it to the first exponent:
\(5^{-9 - (-12)} = 5^{-9 + 12} = 5^{3}\).
Simplifying further, \(5^3\) equals \(5 \times 5 \times 5 = 125\).
Thus, \(5^{-9} \div 4^{-12}\) is equal to \(125\).
To divide two numbers with the same base but different exponents, we subtract the exponents. So, the expression can be rewritten as \(5^{-9 - (-12)}\).
To subtract the exponents, we change the sign of the second exponent and add it to the first exponent:
\(5^{-9 - (-12)} = 5^{-9 + 12} = 5^{3}\).
Simplifying further, \(5^3\) equals \(5 \times 5 \times 5 = 125\).
Thus, \(5^{-9} \div 4^{-12}\) is equal to \(125\).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.