Simplify the following expressions: 1) $b^{-2}c^{-8}$ 2) $42(xa)^2 - 16(xa)^2$ 3) $9.9a + 3.92a$
Understand the Problem
The question asks to simplify the algebraic expressions provided. This involves combining like terms and applying exponent rules where applicable.
Answer
1. $\frac{1}{b^2c^8}$ 2. $16x^{2a}$ 3. $13.82a$
Answer for screen readers
- $\frac{1}{b^2c^8}$
- $16x^{2a}$
- $13.82a$
Steps to Solve
- Simplify the first expression
The first expression is $b^{-2}c^{-8}$. Since the exponents are negative, we can rewrite this as a fraction: $$b^{-2}c^{-8} = \frac{1}{b^2c^8}$$
- Simplify the second expression
The second expression is $16 (x^a)^2$. To simplify this, we use the power of a power rule, which states that $(x^m)^n = x^{m \cdot n}$.
Applying that rule, we get: $$16(x^a)^2 = 16x^{2a}$$
- Simplify the third expression
The third expression is $9.9a + 3.92a$. To simplify, we add the coefficients of the like term 'a': $$9.9a + 3.92a = (9.9 + 3.92)a $$ $$= 13.82a$$
- $\frac{1}{b^2c^8}$
- $16x^{2a}$
- $13.82a$
More Information
When simplifying expressions with negative exponents, remember that $x^{-n} = \frac{1}{x^n}$. Also, when raising a power to another power, multiply the exponents.
Tips
A common mistake is to add the exponents when raising a power to a power, instead of multiplying them. For example, $(x^2)^3$ is often incorrectly simplified to $x^5$ instead of the correct $x^6$. Another common mistake is not combining like terms correctly, for instance, adding only the whole numbers and forgetting the decimal portions.
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