Question - Simplifying Algebraic Expressions with Exponents
mathsimplify algebraic expressionsexponents in algebrapower rule in algebradivision of algebraic terms
Solution:
The given expression is:$$(8a^4x^2y^2)^2 \div a^6x^2y^{-1}$$To solve it, we will first apply the power to the terms inside the parentheses and then divide by the terms outside the parentheses.Applying the power of 2 to each term inside the parentheses:$$= (8^2 \cdot (a^4)^2 \cdot (x^2)^2 \cdot (y^2)^2)$$Calculating each term separately:$$8^2 = 64$$$$(a^4)^2 = a^{4 \cdot 2} = a^8$$$$(x^2)^2 = x^{2 \cdot 2} = x^4$$$$(y^2)^2 = y^{2 \cdot 2} = y^4$$So after applying the power we have:$$= 64a^8x^4y^4$$Now we will divide this by $$a^6x^2y^{-1}$$:$$= \frac{64a^8x^4y^4}{a^6x^2y^{-1}}$$Dividing each term:$$64$$ is just a constant, so it stays as is.For $$a$$, we subtract exponents (when dividing with the same base, subtract the exponents): $$a^{8-6} = a^2$$.For $$x$$, similarly: $$x^{4-2} = x^2$$.For $$y$$, we add the exponents because one of them is negative: $$y^{4-(-1)} = y^{4+1} = y^5$$.So the simplified expression is:$$= 64a^2x^2y^5$$This is the final answer.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com