Simplify the following expressions using exponent rules: (x4)5, (3x2)3, and (y11y7)2.

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Simplify. (Continuing from previous response) ex) (x⁴)⁵ Step 1: Apply the power of a power rule, (a^m)ⁿ = a^(m × n). x^(4 × 5) Step 2: Simplify the exponent. x²⁰ The simplified form is x²⁰. B) (3x²)³ Step 1: Apply the power to each factor inside the parenthesis, (ab)ⁿ = aⁿ bⁿ. 3³ × (x²)³ Step 2: Calculate 3³. 27 × (x²)³ Step 3: Apply the power of a power rule, (a^m)ⁿ = a^(m × n). 27x^(2 × 3) Step 4: Simplify the exponent. 27x⁶ The simplified form is 27x⁶. d) ((y¹¹)/(y⁷))² Step 1: Simplify the expression inside the parenthesis using the division rule for exponents, (a^m)/(aⁿ) = a^(m−n). (y¹¹⁻⁷)² Step 2: Simplify the exponent inside the parenthesis. (y⁴)² Step 3: Apply the power of a power rule, (a^m)ⁿ = a^(m × n). y^(4 × 2) Step 4: Simplify the exponent. y⁸ The simplified form is y⁸.

Simplify the following expressions using exponent rules: (x4)5, (3x2)3, and (y11y7)2.

Step-by-step solution

Apply the power of a power rule, $(a^m)^n = a^{m \times n}$ .

Simplify the exponent.

Apply the power to each factor inside the parenthesis, $(ab)^n = a^n b^n$ .

Calculate $3^3$ .

Apply the power of a power rule, $(a^m)^n = a^{m \times n}$ .

Simplify the exponent.

Simplify the expression inside the parenthesis using the division rule for exponents, $\frac{a^m}{a^n} = a^{m-n}$ .

Simplify the exponent inside the parenthesis.

Apply the power of a power rule, $(a^m)^n = a^{m \times n}$ .

Simplify the exponent.

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More Mathematics Questions

Simplify the following expressions using exponent rules: (x4)5, (3x2)3, and (y11y7)2.

Step-by-step solution

Apply the power of a power rule, (am)n=am×n(a^m)^n = a^{m \times n}(am)n=am×n.

Simplify the exponent.

Apply the power to each factor inside the parenthesis, (ab)n=anbn(ab)^n = a^n b^n(ab)n=anbn.

Calculate 333^333.

Apply the power of a power rule, (am)n=am×n(a^m)^n = a^{m \times n}(am)n=am×n.

Simplify the exponent.

Simplify the expression inside the parenthesis using the division rule for exponents, aman=am−n\frac{a^m}{a^n} = a^{m-n}anam​=am−n.

Simplify the exponent inside the parenthesis.

Apply the power of a power rule, (am)n=am×n(a^m)^n = a^{m \times n}(am)n=am×n.

Simplify the exponent.

Still stuck on this one?

More Mathematics Questions

Apply the power of a power rule, $(a^m)^n = a^{m \times n}$ .

Apply the power to each factor inside the parenthesis, $(ab)^n = a^n b^n$ .

Calculate $3^3$ .

Apply the power of a power rule, $(a^m)^n = a^{m \times n}$ .

Simplify the expression inside the parenthesis using the division rule for exponents, $\frac{a^m}{a^n} = a^{m-n}$ .

Apply the power of a power rule, $(a^m)^n = a^{m \times n}$ .