Simplifying Algebraic Equations

I can't understand how to simplify the equations for example 7x to the 3rd power times 3y to the 2nd power. I am not sure how to simplify them. Can anyone please help me?

Finding the intersection point between two hikers.

Ronald and Rosa are hiking. Ronald hikes 4 miles per hour. Rosa hikes 5 miles per hour. Ronald leaves camp at 8 am for the trail. Rosa leaves camp at 10 am for the trail. At what time will Rosa catch up to Ronald? Where will they be on the trail? How many miles will they be from camp? If they keep hiking for another 2 hours, how ...continues

Determining the distance between two runners at a specific point in time.

Tony and Maria are training for a race by running all the way up and down a 700m long ski slope. They each run up the slope at different constant speeds. Coming down the slope, each runs at double his or her uphill speed. Maria reaches the top first, and immediately starts running back down, meeting Tony 70m from the top. When M ...continues

Finding the solution, the intersection point, between two equations.

What is the value of y to make both solutions equal to each other? x-4=y 4x+2=y

Finding the solution, the intersection point, between two equations.

What value of y will make both equations true? x-4=y 4x+2=y

Understanding and solving exponential equations.

Solve for x: 10^x + 6(10^-x) = 7 and also: 3^3x+2 * 8^-x = 4

Simplifying mathematical expressions.

Find and simplify each of the following values: a)f(-a) b)f(a^-1) c)f(sqrt a) d) F(a^2) Question: f(x)=sqrt 1+x^2+x^4

Calculating the point of intersection between a jet and an airplane.

A private airplane leaves an airport and flies due south at 192 km/h. Two hours later a jet leaves the same airport and flies due south at 960 km/h. When will the jet overtake the plane?

Understanding ratios and proportion.

What are ratios and proportions?

Linear programming : Finding the minimum machine cost

Two machines produce the same item. Machine A can produce 15 items per/hr and Machine B can produce 10/hr. At least 420 of the items must be produced each 40-hr. week, but the machines cannot be operated at the same time. If it costs $50 per hour to operate A and $30 per hour to operate B, determine how many hours per week to o ...continues