Simplify. Rewrite the expression in the form x^(n). x^(2)*x^(-12)=

Identify base and exponents: Identify the base and the exponents of the terms in the expression. In x^(2)*x^(-12), x is the base raised to the exponent 2 in the first term and to the exponent -12 in the second term. Base: x Exponent 1: 2 Exponent 2: -12Apply product rule for exponents: Apply the product rule for exponents, which states that when multiplying two powers that have the same base, you can add the exponents. So, x^(2)*x^(-12) becomes x^(2 + (-12)).Perform addition of exponents: Perform the addition of the exponents. 2 + (-12) equals -10.Write expression with combined exponent: Write the expression with the combined exponent. x^(2)*x^(-12) simplifies to x^(-10).Check for mathematical errors: Check for any mathematical errors in the previous steps. There are no errors in the calculations or application of exponent rules.

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Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Simplify.

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Rewrite the expression in the form

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x^{(n)}.

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x^{(2)}\cdot x^{(-12)}=

Identify base and exponents: Identify the base and the exponents of the terms in the expression. In $x^{2}\times x^{-12}$ , $x$ is the base raised to the exponent $2$ in the first term and to the exponent $-12$ in the second term. $\newline$ Base: $x$ $\newline$ Exponent $1$ : $2$ $\newline$ Exponent $2$ : $-12$
Apply product rule for exponents: Apply the product rule for exponents, which states that when multiplying two powers that have the same base, you can add the exponents. So, $x^{2}\times x^{-12}$ becomes $x^{2 + (-12)}$ .
Perform addition of exponents: Perform the addition of the exponents. $2 + (-12)$ equals $-10$ .
Write expression with combined exponent: Write the expression with the combined exponent. $x^{2}\times x^{-12}$ simplifies to $x^{-10}$ .
Check for mathematical errors: Check for any mathematical errors in the previous steps. There are no errors in the calculations or application of exponent rules.