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Chapter 0: Problem 43

Simplify each exponential expression. $$\left(-3 x^{2} y^{5}\right)^{2}$$

Short Answer

Expert verified
The simplified form of \((-3 x^{2} y^{5})^{2}\) is \(9 * x^{4} * y^{10}\)

Step by step solution

01

Apply Exponent Rule

Follow the exponent rule that says \((ab)^n = a^n * b^n\). Let's apply this rule to \( (-3 x^{2} y^{5})^{2} \). This rule allows us to separately apply the square to each part of the expression within the parenthesis. Doing so, we get: \[ (-3)^{2} * (x^{2})^{2} * (y^{5})^{2} \]
02

Calculate Each Part

Evaluate each part of the expression separately. The square of -3 is 9. Applying the rule that says \((a^n)^m = a^(n*m)\), we get \(x^{2*2}\) and \(y^{5*2}\). Calculate these to simplify the expression to: \[ 9 * x^{4} * y^{10} \]

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Most popular questions from this chapter

Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}+3 x, \text { for } x=8$$

Your local electronics store is having an end-of-the-year sale. The price on a plasma television had been reduced by \(30 \% .\) Now the sale price is reduced by another \(30 \%\). If \(x\) is the television's original price, the sale price can be modeled by $$(x-0.3 x)-0.3(x-0.3 x)$$ a. Factor out \((x-0.3 x)\) from each term. Then simplify the resulting expression. b. Use the simplified expression from part (a) to answer these questions. With a \(30 \%\) reduction followed by a \(30 \%\) reduction, is the television selling at \(40 \%\) of its original price? If not, at what percentage of the original price is it selling?

$$\text { Factor completely.}$$ $$(y+1)^{3}+1$$

$$\text { Factor completely.}$$ $$x^{4}-5 x^{2} y^{2}+4 y^{4}$$

Rewrite each expression without absolute value bars. $$|-203|$$
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