The expression (x^12)(y^-13)(x^-5)(y^4) is equivalent to x^m y^n.

Question

What is the value of n?

Answer 1

Keep in mind this fact: a^j • a^k = a^j+k

This says the multiplication of two powers of some number a, can be found by raising that number to the sum of those two exponents.

(y^-13)(y⁴) = y^-13+4 = y^-9

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An example to illustrate why this is so. The exponent is just how many times to carry out

the multiplication of a number:

4³ = 4•4•4

4⁵ = 4•4•4•4•4

4³•4⁵ = (4•4•4)•(4•4•4•4•4) = 4•4•4•4•4•4•4•4 = 4⁸ (looking at the exponents: 3+5 = 8)

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Some more properties of exponents:

→ A negative exponent is just the reciprocal of the postive exponent: a^-n = 1/aⁿ

→ (aⁿ)^m = a^nm (a number raised to some power, all raised to another power, is that number raised to the product of those powers)

→ Where it gets less obvious is when you see fractional exponents. a^1/2 = √a

This can be derived by using the power rule above: write (a^1/2)^k = a and ask what value of k gives you back a? (1/2)•k = 1 ==> k = 2 so (a^1/2)(a^1/2) = a ==> a^1/2 is the square root of a

More generally, a^n/m = the m^th root of aⁿ

Answer 2

When multiplying variables —> add exponents

-13+4= -9 since these are the exponents for y.

Thus, n=-9.