Question Video: Evaluating Expressions with Multiple Variables and Variable Exponents | Nagwa Question Video: Evaluating Expressions with Multiple Variables and Variable Exponents | Nagwa

Question Video: Evaluating Expressions with Multiple Variables and Variable Exponents Mathematics • Second Year of Preparatory School

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Evaluate π‘₯^𝑧 βˆ’ 𝑧^π‘₯, where π‘₯ = 4 and 𝑧 = 3.

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Video Transcript

Evaluate π‘₯ to the 𝑧 power minus 𝑧 to the π‘₯ power, where π‘₯ equals four and 𝑧 equals three.

We’re given the algebraic expression π‘₯ to the 𝑧 power minus 𝑧 to the π‘₯ power. It’s possible at this point that you might think π‘₯ to the 𝑧 power minus 𝑧 to the π‘₯ power must be zero. However, this is not true. π‘₯ to the 𝑧 power does not equal 𝑧 to the π‘₯ power. They are not additive inverses of each other. And we can confirm this by plugging in the values that we were given for π‘₯ and 𝑧. Since we know that π‘₯ equals four and 𝑧 equals three, our first term will be four cubed and our second term will be three to the fourth power. Four cubed is equal to 64, and three to the fourth power equals 81. This expression would then be 64 minus 81, which equals negative 17. And we see here that four cubed, π‘₯ to the 𝑧 power, does not have the same value as three to the fourth power, 𝑧 to the π‘₯ power.

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