How do you write #5t^-3*3t^-8# using only positive exponents?

Answer 1

Savannah Anderson

Initially, this expression can be rewritten as:

#(5 * 3)(t^-3 * t^-8) = 15(t^-3 * t^-8)#

Next, use this rule for exponents to combine the #t# terms:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#15(t^color(red)(-3) xx t^color(blue)(-8)) = 15t^(color(red)(-3) + color(blue)(-8)) = 15t^-11#

Now, remove the negative exponent by applying this exponents rule:

#x^color(red)(a) = 1/x^color(red)(-a)#

#15t^color(red)(-11) = 15/t^color(red)(- -11) = 15/t^11#

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Answer 2

Savannah Anderson

To write (5t^{-3} \times 3t^{-8}) using only positive exponents, you can rewrite it as (\frac{5}{t^3} \times \frac{3}{t^8}). Then, you can simplify it as (\frac{5 \times 3}{t^3 \times t^8}), which equals (\frac{15}{t^{3+8}}), or simply (\frac{15}{t^{11}}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.