If m and n are positive integers, then xm xn = xm + n In other words, when multiplying two Remember that a fraction bar also indicates division, so a negative sign in front of a fraction goes with the numerator, the denominator, or the whole fraction: \(-\frac{3}{4}=\frac{-3}{4}=\frac{3}{-4}\). Do you notice a relationship between the exponents? In practice, though, this rule means that some exercises may be a lot easier than they may at first appear: Who cares about that stuff inside the square brackets? You may remember that when you divided fractions, you multiplied by the reciprocal. Now that I know the rule (namely, that I can add the powers on the same base), I can start by moving the bases around to get all the same bases next to each other: Now I want to add the powers on the a's and the b's. \(\begin{array}{c}4\cdot{\frac{3[5+{(2 + 3)}^2]}{2}}\\\text{ }\\=4\cdot{\frac{3[5+{(5)}^2]}{2}}\end{array}\), \(\begin{array}{c}4\cdot{\frac{3[5+{(5)}^2]}{2}}\\\text{}\\=4\cdot{\frac{3[5+25]}{2}}\\\text{ }\\=4\cdot{\frac{3[30]}{2}}\end{array}\), \(\begin{array}{c}4\cdot{\frac{3[30]}{2}}\\\text{}\\=4\cdot{\frac{90}{2}}\\\text{ }\\=4\cdot{45}\\\text{ }\\=180\end{array}\), \(4\cdot{\frac{3[5+{(2 + 3)}^2]}{2}}=180\). For example, to solve 2x 5 = 8x 3, follow these steps:\r\n
- \r\n \t
- \r\n
Rewrite all exponential equations so that they have the same base.
\r\nThis step gives you 2x 5 = (23)x 3.
\r\n \r\n \t - \r\n
Use the properties of exponents to simplify.
\r\nA power to a power signifies that you multiply the exponents. We have to do it for each factor inside the parenthesis which in this case are a and b. This expression has two sets of parentheses with variables locked up in them. ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8985"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"
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