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What is the missing number in this simplified exponential expression?

[tex]\[ 7^? \div 7^5 = 7^{12} \][/tex]

(1 point)

[tex]\[ \square \][/tex]


Sagot :

To find the missing number in the given exponential expression \(7^? \div 7^5 = 7^{12}\), let's follow these steps:

1. Understand the properties of exponents: When you divide two expressions with the same base, you subtract the exponent of the divisor from the exponent of the dividend. Mathematically, this property is expressed as:

[tex]\[ \frac{a^m}{a^n} = a^{m-n} \][/tex]

2. Apply this property to the given problem: In this problem, we are working with the base \(7\). The given expression is:

[tex]\[ \frac{7^?}{7^5} = 7^{12} \][/tex]

3. Set up the equation by using the property: According to the property, the division of \(7^?\) by \(7^5\) can be rewritten with a single exponent:

[tex]\[ 7^{?-5} = 7^{12} \][/tex]

4. Equate the exponents: Because the bases are the same (\(7\)), we can equate the exponents from both sides of the equation:

[tex]\[ ? - 5 = 12 \][/tex]

5. Solve for the missing exponent: To find the value of \(?\), solve the equation:

[tex]\[ ? - 5 = 12 \][/tex]

Add \(5\) to both sides of the equation:

[tex]\[ ? = 12 + 5 \][/tex]

[tex]\[ ? = 17 \][/tex]

Therefore, the missing number in the expression [tex]\(7^? \div 7^5 = 7^{12}\)[/tex] is [tex]\(17\)[/tex].